Asymptotics of Weil–Petersson Geodesics II: Bounded Geometry and Unbounded Entropy
Asymptotics of Weil–Petersson Geodesics II: Bounded Geometry and Unbounded Entropy
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Weil-Petersson 测地线 II 的渐进：有界几何和无界熵
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Y. Minsky
中科院分区：
文献类型：
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作者：
Jeffrey F. Brock;H. Masur;Y. Minsky
我们使用Weil-Petersson测地线的结束分层来建立Weil-Petersson测地线的有界几何等价于Weil-Petersson测地线段、射线和线的有界组合。进一步，一个更一般的非环形有界组合的概念，它允许任意大的dehn -扭转，对应于Weil-Petersson测地线的等价条件。作为一个应用，我们证明了weil - petersson测地流具有具有任意大拓扑熵的紧致不变子集。
We use ending laminations for Weil–Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for Weil–Petersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equivalent condition for Weil–Petersson geodesics. As an application, we show theWeil–Petersson geodesic flow has compact invariant subsets with arbitrarily large topological entropy.